w(3w+2)=36

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Solution for w(3w+2)=36 equation:


Simplifying
w(3w + 2) = 36

Reorder the terms:
w(2 + 3w) = 36
(2 * w + 3w * w) = 36
(2w + 3w2) = 36

Solving
2w + 3w2 = 36

Solving for variable 'w'.

Reorder the terms:
-36 + 2w + 3w2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 2w + 3w2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-12 + 0.6666666667w + w2 = 0

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 0.6666666667w + 12 + w2 = 0 + 12

Reorder the terms:
-12 + 12 + 0.6666666667w + w2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 0.6666666667w + w2 = 0 + 12
0.6666666667w + w2 = 0 + 12

Combine like terms: 0 + 12 = 12
0.6666666667w + w2 = 12

The w term is 0.6666666667w.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667w + 0.1111111112 + w2 = 12 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667w + w2 = 12 + 0.1111111112

Combine like terms: 12 + 0.1111111112 = 12.1111111112
0.1111111112 + 0.6666666667w + w2 = 12.1111111112

Factor a perfect square on the left side:
(w + 0.3333333334)(w + 0.3333333334) = 12.1111111112

Calculate the square root of the right side: 3.48010217

Break this problem into two subproblems by setting 
(w + 0.3333333334) equal to 3.48010217 and -3.48010217.

Subproblem 1

w + 0.3333333334 = 3.48010217 Simplifying w + 0.3333333334 = 3.48010217 Reorder the terms: 0.3333333334 + w = 3.48010217 Solving 0.3333333334 + w = 3.48010217 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + w = 3.48010217 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + w = 3.48010217 + -0.3333333334 w = 3.48010217 + -0.3333333334 Combine like terms: 3.48010217 + -0.3333333334 = 3.1467688366 w = 3.1467688366 Simplifying w = 3.1467688366

Subproblem 2

w + 0.3333333334 = -3.48010217 Simplifying w + 0.3333333334 = -3.48010217 Reorder the terms: 0.3333333334 + w = -3.48010217 Solving 0.3333333334 + w = -3.48010217 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + w = -3.48010217 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + w = -3.48010217 + -0.3333333334 w = -3.48010217 + -0.3333333334 Combine like terms: -3.48010217 + -0.3333333334 = -3.8134355034 w = -3.8134355034 Simplifying w = -3.8134355034

Solution

The solution to the problem is based on the solutions from the subproblems. w = {3.1467688366, -3.8134355034}

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